The line with equation y = mx is a tangent to the circle C₁ with equation
(x+4)² + (y-7)² = 13.
(a) Show that m satisfies the equation
3m² + 56m +36=0.
The tangents from the origin O to C₁ touch C₁ at the points A and B.
(b) Find the coordinates of the points A and B.
Another circle C₂ has equation x² + y² = 13. The tangents from the point (4, -7) to C₂ touch it at
the points P and Q.
(c) Find the coordinates of either the point P or the point Q.